Borbala Gerhat
Institute of Science and Technology Austria
Am Campus 1
3400 Klosterneuburg
Austria
borbala.gerhat(at)ista.ac.at
I am currently an MSCA Fellow at the Institute of Science and Technology Austria (AT) under the supervision of Prof. Robert Seiringer.
Research interests
Functional analysis, (non-self-adjoint) operator and spectral theory, operator families, operator matrices, PDEs, generalised form methods, representation theorems, Schrödinger operators, discrete Hardy type inequalities
Publications
On the point spectrum in the Ekman boundary layer problem
Communications in Mathematical Physics (2022) Vol. 392, p. 377-397
(with O. O. Ibrogimov and P. Siegl)Pseudo numerical ranges and spectral enclosures
Complex Analysis and Operator Theory (2022) Vol. 16, No. 78
(with C. Tretter, arXiv)Schur complement dominant operator matrices
Journal of Functional Analysis (2024) Vol. 286, No. 110195
(arXiv)Schrödinger operators with accretive potentials in weighted spaces
(with P. Siegl, preprint)An improved discrete Rellich inequality on the half-line
Israel Journal of Mathematics (to appear)
(with D. Krejčiřík and F. Štampach, arXiv)Criticality transition for positive powers of the discrete Laplacian on the half line
(with D. Krejčiřík and F. Štampach, submitted, arXiv)
Invited conference / workshop talks
Analytic and algebraic methods in physics
Aug 2023, Czech Technical University in Prague (CZ)
Powers of discrete Laplacians and Hardy-type inequalitiesWOTCA and YRFAMP'23
Jul 2023, Universidade de Évora (PL)
Criticality analysis of powers of the discrete LaplacianChallenges in Spectral Theory of Differential Operators
Dec 2022, Graz University of Technology (AT)
Schrödinger operators with accretive potentials in weighted spacesMathematical aspects of the physics with non-self-adjoint operators
Jul 2022, Banff International Research Station (CA)
Schur complement dominance with applications to damped wave equationsWOTCA and YRFAMP'22
Jun 2022, Universidade do Algarve, Faro (PL)
Pseudo numerical rangesChallenges in Non-self-adjoint Spectral Theory
Dec 2019, Queen's University Belfast (UK)
Schur complement dominant operator matrices
Selected contributed talks / seminars
7th Najman Conference on Spectral Theory and Differential Equations
Sep 2023, Brijuni (HR)
Powers of discrete Laplacians and Hardy-type inequalitiesWorkshop Differential-Algebraic Equations and Operator Pencils
Apr 2023, Banff International Research Station (CA)
Dominant Schur complementsNov 2022, Graz University of Technology (AT)
An improved discrete Rellich inequality on the half-lineFunctional analysis, operator theory and dynamical systems
Nov 2022, University of Leipzig / Potsdam (online)
An improved discrete Rellich inequality on the half-lineIX Partial differential equations, optimal design and numerics
Aug 2022, Centro de Sciencias de Benasque Pedro Pascual (SP)
Schur complement dominance with applications to damped wave equationsNov 2020, Queen's University Belfast (UK)
Spectrum of the Ekman boundary layer problemDec 2019, Czech Technical University in Prague (CZ)
Schur complement dominant operator matricesMar 2018, University of Bern (CH)
Holomorphic families and spectral inclusion
Weihnachtskolloquium
Dec 2017, Vienna University of Technology (AT)
Quadratic numerical range and spectral enclosure
Operator Theory and Indefinite Inner Product Spaces
Dec 2016, Vienna University of Technology (AT)
The Krein-Rutman Theorem
Teaching
Czech Technical University in Prague 2023
Calculus II
Queen's University Belfast 2019 - 2020
Numbers, Vectors and Matrices
University of Bern 2017 - 2020
Operator Theory
Advanced Analysis
Functional Analysis
Ordinary Differential Equations
Mathematics in Economy and Social Sciences I, II
Mathematics in Biology I
Vienna University of Technology 2010 - 2012
Analysis II, III
Mathematics in Engineering I, II
Employment
2024 - currently MSCA fellow at the Institute of Science and Technology Austria (AT) under supervision of Prof. R. Seiringer
2022 - 2024 postdoc of Prof. D. Krejčiřík at the Czech Technical University in Prague (CZ) within EXPRO grant of the Czech National Science Foundation
Education
2021 - PhD degree in Mathematics (supervised by C. Tretter), University of Bern (CH)
2019 - SEMP research internship, Queen's University Belfast (UK)
2016 - Master's degree in Technical Mathematics, Vienna University of Technology (AT)
2014 - Erasmus student exchange, Université Paris Dauphine (FR)
2012 - Bachelor's degree in Technical Mathematics, Vienna University of Technology (AT)